Mutual Backscratchability Report

Grade Trade Opportunities

This tool will help you find opportunities to scratch your mutual backs. An opportunity is displayed as a cycle of names connected with arrows. An arrow from A to B (e.g. A → B) means A can grade the group B belongs to. All opportunities are cycles. So everyone involved finds a back to scratch, and someone to scratch their own back, even if the two happen to be different people.

If you have a preference to trade with your friends first, we can accomodate that too! Enter their name(s), (upto 3 other people) and the tool will find you cycles that contain all of the specified people. Happy trading!!! Praise be to the invisible hand!

Who's looking to trade? (Mandatory): Who do you want to trade with? (Optional): Any third person to be added in the same trade? (Optional): Any fourth person to be added in the same trade? (Optional):

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Some Interesting Stuff

The following is a visualization of the how well each group can negotiate. Each node is a group and the arrows connecting them (A → B) show how many members from A can grade B.

The first thing to catch the eye here is that some groups have arrows leading back to themselves!! After running some additional checks I found 31/78 of the folks in our class have been endowed with overly long arms that allow self-back self-scratching. Not all groups (incl. mine) are lucky enough to have had members assigned to grade ourselves though. So the details of these lucky long armed people and their groups are attached below.

Also the sizes of the nodes are different, based on how lucky they have gotten. The size is an increasing function of (# of grading others + # of self-grading - # of being graded by others)